US8763751B2 - Silencer for an auxiliary power unit of an aircraft - Google Patents

Abstract

A silencer for an auxiliary power unit of an aircraft comprises an inlet, an outlet, a housing and a flow channel with a porous wall material that is arranged in the housing. An intermediate space is formed between the housing and the flow channel and divided into outer cells that are arranged around the flow channel by means of one or more partitions. This makes it possible to realize a very compact silencer with very good sound insulation properties. The sound dampening can be additionally improved by dividing the outer cells into outer regions and inner regions, by adapting the shape of the silencer to a tail section of an aircraft and by arranging an annular channel on the outlet.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a national phase entry under 35 U.S.C. §371 of International Application No. PCT/EP2009/063206, filed Oct. 9, 2009, published in German, which claims the benefit of the filing date of German Patent Application No. 10 2008 051 241.9, filed Oct. 10, 2008, U.S. Provisional Patent Application No. 61/195,835, filed Oct. 10, 2008, German Patent Application No. 10 2009 006 579.2, filed Jan. 29, 2009, and U.S. Provisional Patent Application No. 61/148,328, filed Jan. 29, 2009, the entire disclosures of which are hereby incorporated herein by reference.

TECHNICAL FIELD OF THE INVENTION

The invention pertains to a silencer for an auxiliary power unit of an aircraft with a housing and a flow channel arranged in the housing, wherein the intermediate space between the flow channel and the housing is divided into several cells. The invention furthermore pertains to the utilization of a silencer for an auxiliary power unit in an aircraft, as well as to an aircraft with at least one auxiliary power unit and at least one silencer according to the invention.

BACKGROUND OF THE INVENTION

Commercial aircraft commonly comprise an auxiliary power unit (also referred to as “APU” for “Auxiliary Power Unit”) that is frequently arranged in a tail cone of the aircraft, wherein this auxiliary power unit is designed on the basis of a turbo engine such as, for example, a turbojet engine and supplies the aircraft with compressed air and electric energy. In such an arrangement, the exhaust gas created during the operation is discharged into the surroundings of the aircraft through an exhaust gas outlet in the region of the tail cone such that none of the tail assemblies of the aircraft come in contact therewith, if possible under all conditions encountered while the aircraft is on the ground and in flight. Due to the frequent operation of the auxiliary power unit while the aircraft is on the ground, its noise emission may represent the nuisance for the airport and its surroundings. Silencers that are arranged on the exhaust gas outlet of the auxiliary power unit by means of a corresponding coupling and dampen the exhaust gas noise accordingly are used in order to reduce the noise emission on the ground.

It is known, for example, fromEP 1 398 473 B1 and U.S. Pat. No. 6,772,857 B2 to reduce inflow noises on aircraft engines by means of sound-absorbing layers with a honeycomb structure and a reflector. Although a plurality of differently designed silencers for auxiliary power units are also known from the state of the art, one specific design is given special consideration below.

In this design, a flow channel is provided that connects an exhaust gas inlet to an exhaust gas outlet and is surrounded by a housing. The volume between the housing and the flow channel is divided into several cells by means of intermediate walls (also referred to as partitions), wherein the majority of the partitions is equidistantly arranged along the flow channel. The flow channel is usually composed of a metallic, felt-like material that withstands the temperature and corrosiveness of the exhaust gas and is also porous. This not only makes it possible to route the exhaust gas through the flow channel along its extension in the housing, but also allows an alternating flow transverse thereto through the wall material of the flow channel and into the individual cells such that friction converts sound energy into heat during the passage through the wall material of the flow channel and the exhaust gas noise therefore is reduced.

One problem of known silencers of this design is, for example, an insufficient ratio between the diameter of the flow channel and of the housing such that, for example, the outer diameter of the cells is relatively low by comparison and, in particular, a first occurring transversal mode of the exhaust gas sound therefore can only be weakly dampened. In addition, longer cells are required in order to considerably dampen all occurring transversal modes such that the sound damping efficiency per length unit of the silencer ultimately drops. However, there are also known silencers, in which the diameter of the housing is sufficient such that the first transversal mode can be dampened sufficiently strong, but not the second transversal mode. In broadband noise, the sound energy is predominantly transmitted in the range of resonant frequencies due to the generation of resonant modes in a silencer. Another disadvantage of these known silencers consequently can be seen in that the sound dampening is very low for certain frequency ranges due to standing waves in the silencer.

In the design of a corresponding silencer, the available installation space is very restricted, particularly in aircraft, such that the external dimensions of the silencer cannot be arbitrarily enlarged in order to increase the degree of sound dampening, but rather should always be maintained constant or at least as small as possible.

In the existing designs of silencers for auxiliary power units of an aircraft, improvements with respect to the degree of sound dampening are not readily expected without enlarging the external dimensions of the silencer.

SUMMARY OF THE INVENTION

It may therefore be the object of the invention to propose a silencer for an auxiliary power unit of an aircraft, in which improved sound dampening can be achieved without enlarging the external dimensions of the silencer. Although the silencer should be as compact as possible, it should still allow effective sound dampening in a broad frequency range.

This object is attained with a silencer for an auxiliary power unit of an aircraft according to the characteristics ofindependent claim1. Advantageous additional improvements are disclosed in the dependent claims.

Exhaust gas entering the flow channel through an inlet flows toward an outlet within the flow channel and is discharged into the surroundings of the aircraft at this location. The wall material of the silencer according to the invention is porous—as it is also known from the state of the art—and allows an alternating flow through a wall of the flow channel. While flowing through the porous wall material, part of the sound energy is converted into heat such that a certain noise reduction takes place. The cells distributed along the silencer according to the invention cause this noise reduction to repeat several times such that adequate sound dampening can be achieved.

According to a first aspect of the invention, the silencer according to the invention comprises partitions that divide the silencer into several silencer cells. The cells respectively consist of an outer cell and an inner cell (28-44,52,74), wherein the outer cell is considered to be the partitioned region of the intermediate space between the housing and the flow channel. The inner cell (28-44,52,74) is the region of the flow channel that is enclosed by the outer cell. The partitions are not distributed equidistantly in the silencer according to the invention. The partitions are rather arranged relative to one another in such a way that at least two groups of cells are formed in the intermediate space between the housing and the flow channel. The outer cells of a first group respectively have a length comprised of a first interval and cells of a second group respectively have a length comprised of a second interval, wherein the first and the second interval are adjacent to one another and respectively have a width that essentially corresponds to 0.1-times the hydraulic diameter of the flow channel (6). Consequently, the individual cells differ from one another in such a way that they are suitable for effectively dampening at least the first two or three transversal modes.

Since the partitions do not equidistantly divide the silencer, it is also possible to better take into consideration a propagation of the auxiliary power unit noise with different transversal distribution and with different angles of corresponding velocity vectors. The cells of the individual groups may be arranged in an alternating sequence. The volumetric ratio between the inner and the outer cells in combination with the different cell lengths makes it possible to achieve a higher sound damping efficiency per length unit for broadband noise of an auxiliary power unit of an aircraft.

Several outer cells of the aforementioned dimensional intervals are preferably arranged along the silencer in an alternating, grouped or heterogeneously mixed sequence. The definition of the individual advantageous dimensions as a function of the hydraulic diameter is particularly sensible because the cross sections of the individual components of the silencer according to the invention do not necessarily have to be realized circular or circular over the entire length of the silencer according to the invention. In fact, this definition is also suitable for oval or sectionally flattened silencers.

According to a second aspect of the invention, it is advantageous to realize the silencer according to the invention such that the volumes of the outer cells essentially correspond to 1.0- to 1.2-times the volumes of the corresponding inner cells. Consequently, the porous wall of the flow channel is arranged in a region, in which the radial velocities of at least the first two transversal modes are relatively high, such that not just one of the at least first and second transversal modes can be dampened. This makes it possible to reduce the cell length and therefore the overall length of the silencer according to the invention.

According to an advantageous additional improvement, at least one of the outer cells is divided into an outer region and an inner region by means of an additional porous absorber layer in a cylindrical section of the housing of the silencer according to the invention, namely such that the outer region of the at least one outer cell does not directly communicate with the flow channel via its porous wall material. However, the outer region of the corresponding outer cell is connected to the inner region of the outer cell via the absorber layer, wherein the inner region is connected to the flow channel via the porous wall material of the flow channel. Accordingly, a communication between [the flow channel and] the outer region of the corresponding outer cell is only possible through its inner region via the porous absorber layer and the porous wall of the flow channel. Consequently, sympathetic vibrations are suppressed when air is pressed from the inner region into the outer region of the corresponding outer cell through the absorber layer.

The integration of another porous absorber layer for additionally dividing the outer cells makes it possible to achieve a much more advantageous volumetric ratio between the outer cells and the inner cells, wherein the term inner cells refers to the regions within the flow channel that are respectively enclosed by an outer cell. Due to the improved volumetric ratio and the simultaneously enhanced suppression of sympathetic vibrations, sound dampening superior to that known so far can be achieved with the silencer according to the invention in the same or even a smaller installation space.

In a particularly advantageous additional improvement of the silencer according to the invention, at least two outer cells that are arranged in a cylindrical section of the housing and designed in this way have a length that corresponds to 0.2- to 0.6-times the hydraulic diameter of the flow channel.

It is likewise advantageous that these outer cells respectively have a height that corresponds to 0.3- to 0.45-times the hydraulic diameter of the flow channel. Due to this measure, sympathetic vibrations are additionally suppressed and the degree of sound dampening of the silencer according to the invention is additionally improved.

In another advantageous additional improvement of the silencer according to the invention, the absorber layer is designed for forming helical outer and inner regions.

In an equally advantageous additional improvement of the silencer according to the invention, the absorber layer could be realized in the form of a circular or elliptical cylinder such that the outer regions of the outer cells annularly extend around or adjacent to the inner regions of the outer cells. The absorber layer could alternatively also have a conical shape.

In order to further enhance be advantageous sound-absorbing properties of the silencer according to the invention, the sum of the volumes of all outer regions of an outer cell corresponds to 0.8- to 1.2-times the sum of the volumes of all inner regions of an outer cell.

With respect to improved sound dampening, it is furthermore advantageous that the respective length of the cells of the first group essentially corresponds to 0.3- to 0.4-times the hydraulic diameter of the flow channel.

In an advantageous additional improvement of the silencer according to the invention, the respective length of the cells of the second group advantageously corresponds to 0.4- to 0.5-times the hydraulic diameter.

It would furthermore be conceivable to provide cells that respectively have a length corresponding to 0.2- to 0.3-times the hydraulic diameter. Other groups with different length intervals could conceivably also be provided.

In another advantageous additional improvement of the silencer according to the invention, the flow channel is dimensioned such that the radial velocity components of at least a first and a second transversal mode created in the silencer have a common maximum in the region of the wall of the flow channel. Significantly improved sound dampening is achieved due to this measure.

If the exhaust gas noise of the auxiliary power unit also has high-frequency noise components, it is advantageous to integrate at least one additional cell into the silencer, in which the outer cell has a volume that corresponds to 0.75- to 0.85-times the volume of the inner cell. Due to this measure, the position of the wall of the flow channel is adapted to the radial velocity distribution of the high-frequency noise such that the most effective dampening possible of several transversal modes can also take place at this location.

The wall material of the flow channel is advantageously realized similar to the customary state of the art, i.e., it consists of a metallic felt or a similar heat-resistant, corrosion-resistant and porous material. In this case, the flow resistance of this wall material advantageously should be realized such that it amounts to 0.8- to 1.2-times the basic resistance that, depending on the temperature, amounts to

$R=410·{\left(\frac{293}{T}\right)}^{1,26}\frac{\mathrm{Pa}}{\frac{m}{s}}$

In this case, T is the absolute temperature of the exhaust gas that is indicated in K (Kelvin).

The resistance is generally realized such that the exhaust gas can flow through in a noise-induced fashion and the sound energy is at least in part converted into heat. However, this also means that the resistance needs to be sufficiently high for converting as much sound energy as possible into heat.

It is furthermore particularly advantageous if the housing has in at least one section a conical shape and/or comprises several conical components such that an improved adaptation to the available installation space within the aircraft tail cone can be achieved.

It is furthermore preferred that the partitions comprise drainage holes. These drainage holes preferably are respectively arranged at the lowest point of the partitions and ensure that no fuel or the like can accumulate within the individual cells. If they have a sufficiently small size, the drainage holes are not considered to be acoustically disturbing.

According to an advantageous additional improvement of the silencer according to the invention, the housing and the flow channel are adapted to a tail section of the aircraft in the form of an elongated component in order to improve the installation.

In this additional improvement, the cross section of a rear region of the flow channel and of the housing that surrounds this region of the flow channel continuously changes from a first shape to a second shape, wherein each point in the first cross-sectional shape of the flow channel is spaced apart from a nearest outer contour point by a distance that corresponds to no more than half the hydraulic diameter of the first shape, and wherein each point in the second cross-sectional shape of the flow channel is spaced apart from a nearest outer contour point by a distance that corresponds to no more than one-fourth the hydraulic diameter of the first shape.

This could be realized, e.g., in the form of a fishtail that is flattened and widened toward the outlet end.

Honeycomb materials that form the sound-absorbing lining could be at least partially utilized between the flow channel and the housing in this region of the elongated component.

The cross-sectional areas of the first shape and the second shape are preferably identical, wherein the shape of the cross sections could be realized oval, essentially rectangular or otherwise. In an equally advantageous additional improvement of the silencer according to the invention, the cross-sectional area of the second shape could be smaller than the cross-sectional area of the first shape. Due to this measure, the radial modes of the propagating high-frequency sound waves are deformed and the distance between their vibration node lines is approximately cut in half. Thusly deformed modes cannot propagate into the region of the silencer with the second shape that points toward the outlet and are reflected back into the upstream region with the first shape.

In addition, vibration modes with a smaller number of vibration node lines are dampened better in the downstream region with the narrower second shape because the centers of the noise fields lie closer to the sound-absorbing wall that is formed by the housing, any honeycomb elements and the flow channel.

In another advantageous embodiment of the silencer according to the invention, an intermediate region is situated between the upstream region with the first shape and the downstream region with the second shape, wherein a transition from the first shape to a rectangular cross section and subsequently to the second shape is realized in said intermediate region by means of plane wall surfaces.

It would furthermore be advantageous to turn the main axes of the first shape and the second shape relative to one another such that a better adaptation to the geometry of the aircraft tail section can be realized.

The above-described characteristics pertaining to an advantageous design of an end region of a silencer are generally not limited to cylindrically shaped flow channels and housings of silencers according to the invention, wherein any other round or rectangular cross-sectional shapes could also be provided.

In an advantageous additional improvement of the silencer according to the invention, the outlet of the silencer according to the invention is elongated. An additional annular channel is arranged on the outlet and connected to the outlet channel via at least one opening. The ring channel preferably comprises a plurality of exactly 8 openings that are distributed over the ring channel.

The actual purpose of this ring channel consists of significantly dampening a natural vibration that propagates outward in the outlet in an undisturbed fashion in a first radial mode, namely by inducing vibrations that cancel one another out by means of the openings. A sound wave that enters the annular channel through one of these openings can extend in the ring channel and reach an adjacent opening. When reaching this adjacent opening, the present sound waves already have traveled a certain distance such that the sound waves arriving at the adjacent openings could have an opposite phase referred to the sound waves that extend into the ring channel through the adjacent opening. Consequently, sound wave crests encounter sound wave troughs and cancel one another out with respect to their effect.

This ultimately leads to phases and opposite phases canceling one another out on all openings of the annular channel such that a significant dampening of the natural vibration takes place in the first radial mode. A few known silencers have a resonance window of sorts that is caused by the resonance of longitudinal-radial modes in the outlet within a certain range of the critical frequency of the first radial natural mode. In other words, this means that a frequency band exists, in which the acoustic transmissivity is high and hardly any dampening takes place. The additional ring channel can eliminate or at least diminish this disadvantage. Sympathetic vibrations of the air or the exhaust gas in the outlet are suppressed due to the interference of the resonance noise field within the outlet with noise propagating within the ring channel and the absorption of the acoustic energy within the ring channel.

The ring channel preferably comprises 8 openings that are arranged on an inner circumference of the ring channel such that they are uniformly spaced apart from one another. The openings, if suitably designed, are preferably spaced apart from one another in such a way that the distance between two adjacent openings to be traveled by the sound waves corresponds to a half-wave, i.e., the distance between a phase and an opposite phase. When using a different number of openings within the annular channel, it would also be possible that pairs of openings after the next or pairs of openings that lie farther apart from one another respectively form a phase and an opposite phase. The invention is not limited to embodiments, in which only the sound waves of two directly adjacent openings cancel one another out.

It is furthermore preferred that the openings of the ring channel are covered with a permeable absorption material such that part of the sound energy can already be converted into heat when the sound waves pass through the absorption material due to the resistance of the absorption material.

According to a preferred additional improvement of the silencer according to the invention, the absorption material in the annular channel has an admittance Y that essentially corresponds to the following formula:

$Y=\left[0,5\dots 1,5\right]·\left(\frac{A_N}{\rho ·c}\right)$

In this case, ρ is the atmospheric density, c is the speed of sound, A_Nis the normal cross-sectional area of the annular channel and the expression “ρ·c” is the impedance of the exhaust gas.

According to another advantageous additional improvement of the silencer according to the invention, the annular channel is open on an inner circumference, i.e., on the surface that is directed toward the center of the annular channel, wherein this inner circumference is placed on the outlet of the silencer. The individual openings that connect the annular channel to the outlet therefore are only produced in the outlet itself such that the production costs for manufacturing the annular channel are lowered and its weight is reduced due to a smaller material quantity.

The annular channel is preferably arranged in a central region of the outlet, i.e., between the silencer end and an open end of the outlet, and neither lies flush on the silencer end nor on the open end of the outlet.

The annular channel ultimately may have any normal cross section, wherein the term normal cross section refers to an area that rotates about a center of the annular channel and thusly describes the annular channel. This normal cross section may be rectangular, triangular, cylindrical, conical, arbitrarily curved or realized in other ways. The object of the invention is not limited to any normal cross-sectional shape of the annular channel.

The object of the invention is furthermore attained with an aircraft with at least one auxiliary power unit and at least one silencer according to the invention according to the characteristics of the other independent claim.

BRIEF DESCRIPTION OF THE DRAWINGS

Other characteristics, advantages and possible applications of the present invention result from the following description of exemplary embodiments and the figures. In this respect, all described and/or graphically illustrated characteristics form the object of the invention individually and in arbitrary combinations, namely regardless of their combination in the individual claims or their references to other claims. In the figures, identical or similar objects are furthermore identified by the same reference symbols.

FIG. 1 shows a schematic representation of an silencer according to the invention.

FIGS. 2a+bshow sound pressure and velocity distributions in a cell of the silencer according to the invention.

FIG. 3 shows a schematic representation of the length intervals of the cells.

FIG. 4 shows a schematic representation of another exemplary embodiment of an silencer according to the invention.

FIGS. 5ato5crespectively show differently shaped absorber layers in the outer cells in the form of a silencer detail.

FIGS. 6aand6brespectively show other differently shaped absorber layers in the form of a silencer detail.

FIGS. 7aand7balso respectively show other differently shaped absorber layers in the form of a silencer detail.

FIGS. 8aand8bshow another exemplary embodiment of the silencer according to the invention.

FIG. 9 shows another exemplary embodiment of the silencer according to the invention.

FIG. 10 shows another exemplary embodiment of the silencer according to the invention.

FIG. 11 shows the deformation of radial modes in an elongated component on the end of an silencer according to the invention.

FIG. 12 shows an exemplary silencer with an exemplary annular channel.

FIG. 13 schematically shows phases and opposite phases in an annular channel on the outlet of an arbitrary silencer according to the invention.

FIG. 14 shows an aircraft with at least one auxiliary power unit and at least one silencer according to the invention.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

FIG. 1 shows asilencer2 according to the invention that comprises ahousing4 with one or more exemplarilycylindrical components3 and an exemplarily illustratedconical component5, as well as aflow channel6 that is arranged in thehousing4.Several partitions8 are positioned between theflow channel6 and thehousing4 and arranged obliquely referred to theflow channel6, as well as thehousing4. Theflow channel6 is loosely supported in corresponding openings of thepartitions8. The arrangement of thepartitions8 allows an improved thermal expansibility of thepartitions8 and thesilencer2 according to the invention in general. If thepartitions8 would merely be realized in the form of disk-shaped elements that are arranged perpendicular to theflow channel6 and to thehousing4, theflow channel6, as well as thehousing4, could possibly be destroyed when hot exhaust gas correspondingly acts upon thesilencer2 according to the invention.

Along the extension of thesilencer2 according to the invention, thepartitions8 form severalouter cells10 to26 that respectively enclose aninner cell28 to44.

Hot exhaust gas enters thesilencer2 according to the invention through aninlet46, successively flows through the individualinner cells28 to44 and once again exits thesilencer2 according to the invention through anoutlet48. During this process, sympathetic vibrations with several transversal modes that have velocity vectors extending obliquely referred to the direction, in which thesilencer2 according to the invention extends, are incited in thesilencer2 according to the invention and result in an alternating flow through the porous wall material of theflow channel6. Due to the transverse flow into the individualouter cells10 to26, during which the predetermined flow resistance of the wall material of theflow channel6 is overcome, part of the sound energy is converted into heat such that the exhaust gas noise is reduced. The most broadband reduction possible of the exhaust gas noise is achieved due to the differently adapted distances of theindividual partitions8 from one another and the resulting different volumes of theinner cells28 to44 and theouter cells10 to26.

In order to prevent fuel from accumulating in theouter cells10 to26, some or all partitions comprise one or more drainage holes49 that are advantageously located at the respectively lowest point of thepartitions8.

FIG. 2ashows the sound pressure distribution of the exhaust gas as a function of the radius r in an exemplarily illustratedindividual cell50 with aninner cell52 and anouter cell54. In thecell50, the broken line between theinner cell52 and theouter cell54 represents part of the wall of theflow channel6.FIG. 2bshows the radial velocity distribution as a function of the radius r in thesame cell50.

This illustration indicates that it is necessary to dimension theflow channel6 in such a way that a particularly high radial velocity is achieved on its wall surface, if possible in all occurring transversal modes, in order to realize the best dissipation possible through the wall surface.FIG. 2bshows that the dimensions of theflow channel6 chosen in this illustration are close to optimal because a relatively high radial velocity exists in transversal mode1 (identified as “Mode1”), as well as in transversal mode2 (identified as “Mode2”). Due to this measure, at least the first two transversal modes are optimally taken into consideration.

The resistance of the porous wall surface of theflow channel6 that is permeable to an alternating flow needs to be realized such that a pronounced alternating flow preferably takes place between theinner cell52 and theouter cell54, but the flow resistance should also be so high that friction converts as much sound energy as possible into heat. One potentially advantageous realization of the flow resistance that can be individually adjusted with the material selection, the dimensions of the wall thickness and the like is described in greater detail above in the introduction to the description.

A number line that is exemplarily illustrated inFIG. 3 elucidates how advantageous lengths of theouter cells10 to26 and theinner cells28 to44 can be determined. The number line shows multiples of the hydraulic diameter of theflow channel6 with an exemplarily markedfirst interval56 of a first group, asecond interval58 of a second group and athird interval60 of a third group ofouter cells10 to26. In the context of the present invention, it would also be possible, if applicable, to use different length intervals forouter cells10 to26 and correspondingly shifted boundaries without having to forgo the advantages attained with the invention. The illustration inFIG. 3 merely serves for elucidating the invention with reference to one selected example.

FIG. 4 shows asilencer62 according to the invention that comprises ahousing64 and aflow channel66 arranged in thehousing64. Theflow channel66 extends from aninlet68 to anoutlet10 and is made of a porous material. This material of theflow channel6 could consist, for example, of a metallic felt or a similar material that is realized in a porous or otherwise air-permeable fashion and also maintains its mechanical integrity when it is subjected to high exhaust gas temperatures.

An intermediate space formed between theflow channel66 and thehousing64 is divided in the longitudinal direction of thesilencer62 according to the invention by means ofpartitions72. Eachpartition72 forms a pair of adjacent cells that respectively consist of aninner cell74 and anouter cell76. In this context, aninner cell74 is a section of theflow channel66 that is completely enclosed by anouter cell76 formed by apartition12.

One peculiarity of thepresent silencer62 is that theouter cells76 are additionally divided by means of anotherporous absorber layer78 such that eachouter cell76 has anouter region80 and aninner region82. In this case, theouter region80 is fluidically not directly connected to the correspondinginner cell74, but rather can only communicate with theinner region82 via theporous absorber layer78. Due to the porous design of theflow channel66, however, eachinner region82 is able to communicate with theflow channel66.

Such a design of thesilencer62 according to the invention with an additionalporous absorber layer78 makes it possible to suppress or entirely eliminate sympathetic vibrations induced by the exhaust gas jet passing through theflow channel66.

In the illustrated example, at least two firstouter cells76 and84 have a length that corresponds to 0.2- to 0.6-times thehydraulic diameter88 of theflow channel66. In addition, these at least two firstouter cells76 and84 have aheight90 that corresponds to 0.3- to 0.45-times thehydraulic diameter88 of theflow channel66. It would furthermore be possible to realizeouter cells85 and87 that do not necessarily have to entirely comply with this geometric definition.

With respect to the dimensions of theflow channel6, the description refers to ahydraulic diameter28 because it is not absolutely imperative that thesilencer2 and/or theflow channel6 have/has a circular cross section. In fluid dynamics, however, it is common practice to define a hydraulic diameter for arbitrary cross-sectional shapes of objects, through which a fluid can flow, wherein this hydraulic diameter makes it possible to compare the fluidic properties of said objects.

Another peculiarity of thesilencer62 according to the invention according toFIG. 4 is the fact that afirst section92 of thesilencer62 is realized cylindrically while anotherregion94 of thesilencer2 according to the invention has a conical shape. Due to this measure, a better adaptation to the boundary conditions of the installation space can be achieved.

In the illustrated example, thepartitions68 are arranged obliquely such that an improved thermal expansibility of thepartitions68 and theentire silencer62 according to the invention is achieved. If thepartitions68 would merely be realized in the form of disk-shaped elements that are arranged perpendicular to theflow channel66 and to thehousing64, theflow channel66, as well as thehousing64, could possibly be destroyed when hot exhaust gas correspondingly acts upon thesilencer62 according to the invention.

Thepartitions68 also have the function of holding theflow channel66 that preferably is loosely arranged in corresponding openings of thepartitions68.

The functional principle of the illustratedsilencer62 can basically be described as follows. Hot exhaust gas enters thesilencer62 according to the invention through aninlet68, successively flows through the individualinner cells74 and once again exits thesilencer62 according to the invention through anoutlet70. During this process, sympathetic vibrations with several transversal modes that have velocity vectors extending obliquely referred to the direction, in which thesilencer62 according to the invention extends, are incited in thesilencer62 according to the invention and result in an alternating flow through the porous wall material of theflow channel66. Due to the transverse flow into the individualouter cells76, part of the sound energy is converted into heat such that the exhaust gas noise is reduced. Within theouter cells76, the exhaust gas also flows through theporous absorber layer78, by means of which the corresponding sympathetic vibration is dampened and another part of the sound energy is absorbed and converted into heat.

The most broadband reduction possible of the exhaust gas noise can be achieved due to the differently adapted distances of theindividual partitions72 from one another and the resulting different volumes of theinner cells74 and theouter cells76. Likewise, the entire arrangement of the silencer according to the invention is also able to significantly dampen not only high-frequency noises, but also low-frequency noises, wherein this is achieved with a relatively high volumetric ratio between the outer cells and the inner cells.

In order to prevent fuel from accumulating in theouter cells76, some or allpartitions72 comprise one or more drainage holes96 that are advantageously located, in particular, at the respectively lowest point of thepartitions72 in order to improve the drainage.

The different exemplary embodiments inFIGS. 5ato5c, as well as inFIGS. 6a,6b,7aand7b, indicate that the concrete design and configuration of theporous absorber layer78 can be realized in many different ways.

InFIG. 5a, theporous absorber layer98 conically extends between thehousing64 and theflow channel66 such that theouter cell100 is divided into aninner region42 and anouter region104. Theouter region104 of theouter cell100 cannot directly communicate with theflow channel66, but rather only with the correspondinginner region102 of theouter cell100 via theporous absorber layer98.

Theabsorber layer106 inFIG. 5b, in contrast, has a completely different shape than that illustrated inFIG. 5a. In this case, theabsorber layer106 forms partiallycylindrical sections108 that extend from the wall of theflow channel66 to thehousing64 parallel to the direction, in which thesilencer62 according to the invention extends. In this context, it should be noted that cylindrical does not necessarily refer to the shape of a circular cylinder, but also, for example, to the shape of an elliptical cylinder.

FIG. 5c, in contrast, shows anabsorber layer110 that forms annularouter regions112 and annularinner regions114 between thehousing64 and the wall of theflow channel66. The concrete design can be realized in numerous different ways such that theabsorber layer110 could be realized with an undulated, angular or similar shape in a longitudinal section through thesilencer62.

The exemplary embodiment according toFIGS. 6aand6bshows anabsorber layer116 that forms annularouter regions118 and annularinner regions120 in the intermediate space between theflow channel66 and thehousing64. The illustration according toFIG. 6brepresents a view ofFIG. 6afrom the direction indicated therein with an arrow. In order to identify the configuration of theinner regions120 and theouter regions118, squares and circles that respectively represent the inner region120 (circle) or the outer region118 (square) are drawn into the respective illustration.

FIGS. 7aand7bshow anabsorber layer122 that is essentially realized similar to theabsorber layer116 according toFIGS. 6aand6b, but theinner regions124 and theouter regions126 have a helical or screw-like shape in the intermediate space between theflow channel66 and thehousing4.

Thesilencer128 according to the invention illustrated inFIGS. 8aand8bcomprises aninlet130, anoutlet132 and ahousing134, in which aflow channel136 is arranged. The cross section of the end of theflow channel136 that is connected to theoutlet132 and of the corresponding section of thehousing134 continuously transforms from afirst shape138 into asecond shape140, wherein each point in the firstcross-sectional shape138 of theflow channel136 is spaced apart from a nearest outer contour point of thehousing134 by a distance that corresponds to no more than half the hydraulic diameter of thefirst shape138 of theflow channel136, and wherein each point in the second cross-sectional shape of theflow channel136 is spaced apart from a nearest outer contour point of thehousing134 by a distance that corresponds to no more than one-fourth the hydraulic diameter of thefirst shape138 of theflow channel136. This region could be realized in the form of anelongated component135. A honeycomb material that improves the sound dampening could be arranged between thehousing134 and theflow channel136 of theelongated component135.

According to the top view of thesilencer128 according to the invention illustrated inFIG. 8b, thewidth142 of theelongated component135 could decrease continuously or in stages. The section of thesilencer128 according to the invention that points toward theoutlet132, i.e., downstream, therefore has the approximate shape of a fishtail.

FIG. 9 shows anotherexemplary embodiment142 of a silencer according to the invention that comprises aninlet144 and anoutlet146, between which aflow channel148 extends. The cross section of the flow channel in the region of theoutlet146, e.g., in the form of anelongated component147, as well as the cross section of thehousing150 that surrounds this region of theflow channel148, also changes continuously from afirst shape152 into asecond shape154 in order to ultimately assume athird shape156 in the region of theoutlet146.

The cross section of theflow channel148 in the region of thefirst shape152 is exemplarily illustrated in the form of a circular cross section while theflow channel148 is exemplarily illustrated with a rectangular shape in the region of thesecond shape154 and thethird shape156. For example, theflow channel148 forms straight wall surfaces158 between thesecond shape154 and thethird shape156.FIG. 10 shows the exemplary embodiment according toFIG. 9, in which the main axes of thesecond shape154 and thethird shape156 are turned relative to thefirst shape152. The main axes can be turned in such a way that the outlet points downward, upward or sideward.

FIG. 11 shows deformed radial modes that respectively occur in a region of afirst shape152, asecond shape154 and athird shape156. This figure clearly shows severalnodal lines160, thedistances162,164 and166 of which from one another become smaller as the corresponding sound wave approaches the end of a silencer designed in accordance withFIGS. 8ato10.

In the region of thefirst shape152, thedistance162 between thenodal lines160 is relatively large while thedistance166 between thenodal lines160 in thethird shape156 could approximately correspond to half thedistance162 in the region of thefirst shape152. Thisdistance166 could concretely be smaller than half a wavelength such that the propagation of the sound waves in this rear region of the silencer is reduced or entirely prevented. The centers of the noise fields lie closer to the absorbing wall of therespective housing134 or150.

FIG. 12ashows an additional improvement of a silencer according to the invention. An exemplarily illustratedsilencer168, the shape and internal structure of which are completely irrelevant with respect to the additional improvement of the silencer to be described with reference to the following figures, comprises anelongated outlet170, on which anannular channel172 is arranged. Theannular channel172 could be created, for example, by the rotation of an arbitrarily shaped area that forms thenormal cross section174 about alongitudinal axis176 of thesilencer168.

According toFIG. 12b, theannular channel172 comprisesseveral openings178 that correspond tosuitable openings180 of theoutlet170. For reasons of simplicity, overlappingopenings178 and180 of theoutlet170 are respectively illustrated inFIG. 12b. In the following description, the design of theopenings178 and180 is irrelevant and it merely needs to be ensured that a connection between theoutlet170 and theannular channel172 can be produced.

For example, theopenings178 and180 are uniformly distributed over aninner circumference182 of theannular channel172. In this context, it should be ensured that the phase and the opposite phase of a natural vibration of a first radial mode respectively alternate in twoadjacent openings178 of the annular channel117. Alternatively, it would also be possible to realize other patterns of phases and opposite phases, in which the correspondingopenings178 do not necessarily have to be arranged directly adjacent. Accordingly, it is considered advantageous to arrange an even number ofopenings178 on theannular channel172.

In this case, the area of thenormal cross section174 of theannular channel72 is designed such that a vibration propagates in a region between twoadjacent openings178 in theannular channel172 in such a way that the vibration from theannular channel172 that encounters theadjacent opening178 or the othercorresponding opening178 leads by half an oscillation period and a phase therefore encounters an opposite phase at each opening in order to largely cancel out the vibration phenomena.

According toFIGS. 12c, dande, the cross-sectional shape of theannular channel172 is basically irrelevant.FIG. 12cshows anannular channel184 that has an approximately triangular cross section, wherein the cross section could also be opened on a side that protrudes toward theoutlet170. Accordingly, noseparate opening178 is required in theannular channel184 because theopening180 in theoutlet170 suffices for communicating with theannular channel184.

FIG. 12dshows anannular channel186 that has a closed rectangular cross section.

Furthermore,FIG. 12eshows an oval or ellipticalannular channel188, wherein many more different cross-sectional shapes could also be realized, and wherein the illustrated cross-sectional shapes should not be used for restricting the invention.

The distribution of the pressure in the first radial mode is illustrated inFIG. 13. At resonance, the pressure waves are in phase in allpoints190 to204. A vibration is incited within theannular channel172 by the exemplarily discussed opening190 of theannular channel172 and reaches theadjacent point192 with a phase that depends on the distance between theopenings190 and192. The incited vibration once again reaches theoutlet170 through theopening192. The distance between theopenings190 and192 is calculated in accordance with the following formula that is based on 8 openings190-204:

$L_{190-192}=\pi ·\frac{\mathrm{<figure-callout\; label="D"\; filenames="US08763751-20140701-D00000.png,US08763751-20140701-D00001.png"\; state="\{\{state\}\}">D</figure-callout>}}{8}$
wherein D is the diameter of theoutlet170.

The phase shift therefore is calculated in accordance with

${\mathrm{Fi}}_{190-192}=\frac{2\pi ·{\mathrm{<figure-callout\; label="F"\; filenames="US08763751-20140701-D00001.png,US08763751-20140701-D00002.png"\; state="\{\{state\}\}">F</figure-callout>}}_{1R}·L_{190-192}}{c}$
wherein F_1Ris the critical frequency and c is the speed of sound. The critical frequency is calculated in the form of

${\mathrm{<figure-callout\; label="F"\; filenames="US08763751-20140701-D00001.png,US08763751-20140701-D00002.png"\; state="\{\{state\}\}">F</figure-callout>}}_{1R}=\frac{1\text{,}22·c}{D}$
such that the phase shift is calculated in accordance with

${\mathrm{Fi}}_{190-192}=\frac{2,44{\mathrm{<figure-callout\; label="\pi "\; filenames="US08763751-20140701-D00000.png,US08763751-20140701-D00001.png"\; state="\{\{state\}\}">\pi </figure-callout>}}^2}{8}=3\text{,}01\mathrm{rad}\approx \pi$

This means that the vibration from theannular channel172 reaches theoutlet170 from theopening192 with an approximately opposite phase, i.e., Fi_190-192approximately π, and therefore cancels out the vibration of the radial mode.

A similar interference is also achieved for the noise fromother openings204,202 and the like and the radial mode is dampened within theoutlet170 in this fashion.

Accordingly, a total of 8openings178 or180 is considered particularly advantageous for the additional improvement of a silencer according to the invention illustrated inFIGS. 12ato13.

FIG. 14 ultimately shows anaircraft206 with anauxiliary power unit208 that is equipped with a silencer according to the invention. The basic shape and the internal structure of a silencer according to the invention according to one of the above-described exemplary embodiments make it possible to realize a particularly compact shape that still provides very good sound insulation properties. Due to the special shape of the rear end of the silencer in the form of a fishtail, it can be adapted particularly well to a tail section of an aircraft. An additional improvement of the sound insulation properties is achieved by arranging an annular channel on an elongated outlet of an arbitrarily designed silencer.

In contrast to the above-described exemplary embodiments, the silencer according to the invention could also be realized in the form of the following examples:

EXAMPLE 1

A silencer for an auxiliary power unit of an aircraft comprises an inlet, an outlet, a housing and a flow channel that is arranged in the housing, wherein an intermediate space formed between the housing and the flow channel is divided into outer cells arranged around the flow channel by means of one or more partitions and the wall material of the flow channel is porous, wherein the partitions are arranged relative to one another in such a way that at least two outer cells with a respective length that corresponds to 0.2-0.6-times the hydraulic diameter of the flow channel and a respective height that corresponds to 0.3-0.45-times the hydraulic diameter of the flow channel are formed in the intermediate space between the housing and the flow channel in a cylindrical section of the housing, wherein at least one outer cell is divided into an outer region and an inner region by means of a porous absorber layer in the cylindrical section of the housing, and wherein the outer region does not directly communicate with the flow channel.

EXAMPLE 2

A silencer of example 1, in which the housing has a conical shape at least in one section.

EXAMPLE 3

A silencer of example 1 or 2, in which the sum of the volumes of all outer regions of at least one outer cell in the cylindrical section of the housing corresponds to 0.8-1.2-times the sum of the volumes of all inner regions of the same outer cell.

EXAMPLE 4

A silencer of example 1, in which the partitions are arranged relative to one another in the cylindrical section of the housing such that at least two groups of outer cells are formed in the intermediate space between the cylindrical section of the housing and the flow channel, wherein outer cells of a first group respectively have a length comprised of a first interval and outer cells of a second group respectively have a length comprised of a second interval, and wherein the first and the second interval are adjacent to one another and respectively have a width that essentially corresponds to 0.1-times the hydraulic diameter of the flow channel.

EXAMPLE 5

A silencer of example 4, in which the first group of outer cells has a length that corresponds to 0.3-0.4-times the hydraulic diameter of the flow channel.

EXAMPLE 6

A silencer of example 4 or 5, in which the second group of outer cells has a length that corresponds to 0.4-0.5-times the hydraulic diameter of the flow channel.

EXAMPLE 7

A silencer of one of examples 4 to 6, in which an additional third group of outer cells has a length that corresponds to 0.2-0.3-times the hydraulic diameter of the flow channel.

EXAMPLE 8

A silencer of one of the preceding examples, in which the wall material of the flow channel has a flow resistance that corresponds to 0.8- to 1.2-times a basic resistance that is calculated in accordance with

$R=410·{\left(\frac{293}{T}\right)}^{1,26}\frac{\mathrm{Pa}}{\frac{m}{s}}$
wherein T is the temperature of the gas flowing through the silencer expressed in Kelvin (K).

EXAMPLE 9

A silencer of one of the preceding examples, in which at least one partition respectively comprises at least one drainage hole.

EXAMPLE 10

A silencer of one of the preceding examples, in which the porous absorber layer in the cylindrical section of the housing is realized in such a way that the outer regions of the outer cells helically extend around the inner regions of the outer cells.

EXAMPLE 11

A silencer of one of the preceding examples, in which the porous absorber layer in the cylindrical section of the housing is realized in such a way that the outer regions of the outer cells annularly extend around or adjacent to the inner regions of the outer cells.

In addition, silencers realized in accordance with any design known from the state of the art can also be equipped with an elongated outlet and an additional annular channel in order to achieve improved sound dampening.

As a supplement, it should be noted that “comprising” does not exclude any other elements or steps, and that “a” or “an” does not exclude a plurality. It should furthermore be noted that characteristics or steps that were described with reference to one of the above exemplary embodiments can also be used in combination with other characteristics or steps of other above-described exemplary embodiments. Reference symbols in the claims should not be interpreted in a restrictive sense.

List of Reference Symbols

• 2 Silencer
• 3 Cylindrical housing component
• 4 Housing
• 5 Conical housing component
• 6 Flow channel
• 8 Partition
• 10 Outer cell
• 12 Outer cell
• 14 Outer cell
• 16 Outer cell
• 18 Outer cell
• 20 Outer cell
• 22 Outer cell
• 24 Outer cell
• 26 Outer cell
• 28 Inner cell
• 30 Inner cell
• 32 Inner cell
• 34 Inner cell
• 36 Inner cell
• 38 Inner cell
• 40 Inner cell
• 42 Inner cell
• 44 Inner cell
• 46 Inlet
• 48 Outlet
• 49 Drainage hole
• 50 Cell
• 52 Inner cell
• 54 Outer cell
• 56 First interval of a first group
• 58 Second interval of a second group
• 60 Third interval of a third group
• 62 Silencer
• 64 Housing
• 66 Flow channel
• 68 Inlet
• 70 Outlet
• 72 Partition
• 74 Inner cell
• 76 Outer cell
• 78 Porous absorber layer
• 80 Outer region
• 82 Inner region
• 84 Outer cell
• 85 Outer cell
• 86 Length of outer cell
• 87 Outer cell
• 88 Hydraulic diameter
• 90 Height of outer cell
• 92 Region with cylindrical shape
• 94 Region with conical shape
• 96 Drainage hole
• 98 Porous absorber layer
• 100 Outer cell
• 102 Inner region
• 104 Outer region
• 106 Porous absorber layer
• 108 Outer region
• 110 Porous absorber layer
• 112 Outer region
• 114 Inner region
• 116 Porous absorber layer
• 118 Outer region
• 120 Inner region
• 122 Porous absorber layer
• 124 Inner region
• 126 Outer region
• 128 Silencer
• 130 Inlet
• 132 Outlet
• 134 Housing
• 135 Elongated component
• 136 Flow channel
• 138 First shape
• 140 Second shape
• 142 Silencer
• 144 Inlet
• 146 Outlet
• 147 Elongated component
• 148 Flow channel
• 150 Housing
• 152 First shape
• 154 Second shape
• 156 Third shape
• 158 Section
• 160 Nodal line
• 162 Distance
• 164 Distance
• 166 Distance
• 168 Silencer
• 170 Outlet
• 172 Annular channel
• 174 Normal cross section
• 176 Longitudinal axis
• 178 Opening
• 180 Opening
• 182 Inner circumference
• 184 Annular channel
• 186 Annular channel
• 188 Annular channel
• 190 Opening
• 192 Opening
• 194 Opening
• 196 Opening
• 198 Opening
• 200 Opening
• 202 Opening
• 204 Opening
• 206 Aircraft
• 208 APU

Claims (19)

The invention claimed is:

1. A silencer for an auxiliary power unit of an aircraft, comprising:

an inlet;

an outlet;

a housing; and

a flow channel arranged in the housing,

wherein an intermediate space is formed between the housing and the flow channel, the intermediate space being divided into outer cells that are arranged around the flow channel by one or more partitions, wherein a wall material of the flow channel is porous,

wherein the partitions are arranged relative to one another in such a way that at least first and second groups of outer cells are formed in the intermediate space between the housing and the flow channel,

wherein the outer cells of the first group have a length comprised of a first interval and the outer cells of the second group have a length comprised of a second interval,

wherein the first and the second intervals are adjacent to one another and respectively have a width essentially corresponding to 0.1-times the hydraulic diameter of the flow channel, and

wherein the outer cells have a volume corresponding to 1.0-1.2-times the volume of inner cells enclosed by the respective outer cells and formed in the flow channel.

2. The silencer ofclaim 1,

wherein the partitions are arranged relative to one another in such a way that at least two outer cells with a respective length corresponding to 0.2-0.6-times the hydraulic diameter of the flow channel and a respective height corresponding to 0.3-0.45-times the hydraulic diameter of the flow channel are formed in the intermediate space between the housing and the flow channel in a cylindrical section of the housing, and

wherein at least one outer cell is divided into an outer region and an inner region by a porous absorber layer in the cylindrical section of the housing, wherein the outer region is not in direct communication with the flow channel.

3. The silencer ofclaim 2, wherein the porous absorber layer in the cylindrical section of the housing is realized in such a way that the outer regions of the outer cells helically extend around the inner regions of the outer cells.

4. The silencer ofclaim 2, wherein the porous absorber layer in the cylindrical section of the housing is realized in such a way that the outer regions of the outer cells annularly extend around or adjacent to the inner regions of the outer cells.

5. The silencer ofclaim 2, wherein the sum of the volumes of all outer regions of at least one outer cell in the cylindrical section of the housing corresponds to 0.8-1.2-times the sum of the volumes of all inner regions of the same outer cell.

6. The silencer ofclaim 2, wherein the partitions are arranged relative to one another in the cylindrical section of the housing in such a way that at least two groups of outer cells are formed in the intermediate space between the cylindrical section of the housing and the flow channel, wherein the outer cells of a first group respectively have a length comprised of a first interval and the outer cells of a second group respectively have a length comprised of a second interval, and wherein the first and the second intervals are adjacent to one another and respectively have a width that substantially corresponds to 0.1-times the hydraulic diameter of the flow channel.

7. The silencer ofclaim 1, wherein the first group of outer cells has a length corresponding to 0.3-0.4-times the hydraulic diameter of the flow channel.

8. The silencer ofclaim 1, wherein the second group of outer cells has a length corresponding to 0.4-0.5-times the hydraulic diameter of the flow channel.

9. The silencer ofclaim 1, wherein an additional third group of outer cells has a length corresponding to 0.2-0.3-times the hydraulic diameter of the flow channel.

10. The silencer ofclaim 1, wherein the wall material of the flow channel has a flow resistance corresponding to 0.8- to 1.2-times a basic resistance that is calculated in accordance with

$R=410·{\left(\frac{293}{T}\right)}^{1,26}\frac{\mathrm{Pa}}{\frac{m}{s}}$

wherein T is the temperature of the gas flowing through the silencer expressed in Kelvin.

11. The silencer ofclaim 1, wherein at least one partition respectively comprises at least one drainage hole.

12. The silencer ofclaim 1, wherein the housing comprises one or more conical components.

13. The silencer ofclaim 1, wherein the cross section of the flow channel and of at least one section of the housing surrounding the flow channel continuously changes from a first shape to a second shape, wherein each point in the first cross-sectional shape of the flow channel is spaced apart from a nearest outer contour point of the housing by a distance corresponding to no more than half the hydraulic diameter of the first shape, and wherein each point in the second cross-sectional shape of the flow channel is spaced apart from a nearest outer contour point of the housing by a distance corresponding to no more than one-fourth the hydraulic diameter of the first shape.

14. The silencer ofclaim 1, further comprising an annular channel placed on an elongated outlet and communicating with the outlet via at least one opening arranged on the outlet.

15. The silencer ofclaim 14, further comprising a plurality of openings arranged on an inner circumference of the annular channel in such a way that a sound wave entering the annular channel through an opening propagates and reaches an adjacent opening, and wherein the sound wave entering the annular channel from the outlet via the adjacent opening has an opposite phase referred to the sound wave propagating in the annular channel and the phase and the opposite phase cancel one another out at the adjacent opening.

16. The silencer ofclaim 14, wherein the annular channel communicates with the outlet via a plurality of openings uniformly distributed over the outlet.

17. The silencer ofclaim 1, wherein the flow channel is dimensioned such that radial velocity components of at least first and second transversal modes created in the silencer have a common maximum in the region of the wall of the flow channel.

18. The silencer ofclaim 17, further comprising additional outer cells in order to dampen high-frequency noises, and wherein the additional outer cells have a volume that corresponds to 0.75-0.85-times the volume of inner cells that are enclosed by the respective outer cells and formed in the flow channel.

19. A method for making a silencer for an auxiliary power unit of an aircraft, the method comprising:

providing a silencer with an inlet, an outlet, a housing and a flow channel having a porous wall material;

forming an intermediate space between the housing and the flow channel;

dividing the intermediate space into outer cells arranged around the flow channel by one or more partitions; and

arranging the partitions relative to one another in such a way that at least first and second groups of outer cells are formed in the intermediate space between the housing and the flow channel,

wherein the first and the second intervals are adjacent to one another and respectively have a width essentially corresponding to 0.1-times the hydraulic diameter of the flow channel, and

wherein the outer cells have a volume corresponding to 1.0-1.2-times the volume of inner cells enclosed by the respective outer cells and formed in the flow channel.

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